bp Value at Risk An Introduction To Its Use In An Energy Trading Company Krishan Sabharwal Manager, Risk & Analytics BP Energy Company November 7 th , 2003
Jun 08, 2015
bp
Value at RiskAn Introduction To Its Use In An Energy Trading Company
Krishan Sabharwal
Manager, Risk & Analytics
BP Energy Company
November 7th, 2003
4
Who We Are
BP. Amoco, ARCO, and Castrol have come together to create one of the largest energy companies on the planet.
Global Presence
8
• we’re the largest gas and oil producer in North America
• we’re fuel for travelers at 1400 airports in 87 countries
• we are among the most profitable petrochemical producers in the world
• we’re the largest marketer of raw materials used to make CD boxes, insulation and other everyday products
• we are the leading solar producer in the world
Performance
Upstream 59% Downstream
23%
Other 2%Chemicals
16%
Capital Employed*$63 Billion
* Excludes liabilities
for current and deferred taxation of
$4 billion for total capital employed of $59 billion
Rank Company 1Q03 1Q02
1 BP 20.1 14.9
2 Mirant 12.6 21.4
3 Coral 9.9 9.2
4 Sempra 9.5 9.5
5 ConocoPhillips 8.8 4.6
6 Cinergy 4.2 3.8
7 Reliant 4.0 10.5
8 Nexen 3.5 2.2
9 Oneok 3.5 2.8
10 Williams 3.5 5.4
Top North American Marketers by Volume (Bcf/d)
Source: Gas Daily
Note: Duke, AEP and Dynegy are no longer reporting volumes; El Paso did not respond to queries
Value at Risk
“Value at risk (VaR) is an attempt to provide a single number for senior management summarizing the total risk in a portfolio of financial assets.” – Hull
JP Morgan’s 4:15 report to senior management
Usually takes the form of “We are X percent certain that we will not lose more than V dollars in the next N days.”• X typically 95 – 99%• N typically 1 day• V typically very large, depending on X and N!
Typical Energy Trading Risk Factors
Natural gas futures prices Natural gas basis (Delivery location price – Futures
Price) Electricity forward market prices Crude oil futures prices Crude products (gasoline, diesel, etc.) prices Coal prices Emission credit prices Interest rates Etc.
Green = Typical BP Energy (Houston) exposures
Definitions of Volatility
1t
tseries
P
PLNStdDevVolatilityDaily
VolatilityDailyVolatilityAnnualized 252
VaRdayNVaRNday 1
VaR Methodologies
Analytic (Variance-Covariance)• RiskMetrics
Monte Carlo Simulation Historical Simulation Stress Testing Principal Components Analysis (w/ MC
Simulation)
Analytic VaR
Benefits:1. Fast
2. Relatively easy to understand
3. Allows for VaR “Greeks” (VaRdelta, Component VaR)
Weaknesses1. Doesn’t handle non-linear (option) portfolios well
2. Highly correlated market exposures can lead to dysfunctional statistics
3. Exposure “bucketing” typical to keep dataset manageable
4. Assumes returns are normally distributed
The Analytic VaR “Bible”
Analytic VaR Example
Analytic VaR Example Cont.
Analytic VaR Example Cont.
Analytic VaR Matrix Math
Monte Carlo VaR
Benefits:1. Handles non-linear (option) portfolios well via full portfolio
valuation
2. Highly correlated market exposures not a problem
3. Relatively easy to understand
Weaknesses1. Doesn’t allow for VaR “Greeks” (VaRdelta, Component VaR)
2. Generally slower than closed-form techniques
3. May require high number of iterations to achieve confidence in results
4. May still require “bucketing”
5. Normal return distribution assumption (typically)
6. The “Monte Carlo” effect!
Monte Carlo VaR Technique
Methodology:1. Estimate volatility of each underlying risk factor in BP
Energy’s portfolio:– Nymex natural gas futures contracts– Basis (physical delivery location – Nymex)– Electricity forward contracts
2. Estimate the correlation of the risk factors:– Intracommodity (June ’02 Nymex gas to July ’02 Nymex
gas)– Cross Commodity (June ’02 Nymex gas to June ’02
Cinergy electricity)– Hybrid (June ’02 Nymex gas to June ’02 Chicago Citygate
gas)
3. Simulate all risk factors & revalue the portfolio for each iteration
Monte Carlo based VaR
Historical Simulation
Benefits:1. No volatility or correlation data required
2. Intuitive – “grounded in reality”
3. Fast
4. Handles non-linear (option) portfolios well via full portfolio valuation
5. Actual return distribution used vs. Normal assumption
Weaknesses:1. “Past returns are not indicative of future results”
2. VaR is a function of historical time period selection – subjective!
3. May be limited historical data for certain commodities
Historical Simulation Cont.
Which Time period would you select?Historic Henry Hub Gas Volatility & Price Levels
(1/1/95 - 12/31/01)
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
01/0
3/95
07/2
2/95
02/0
7/96
08/2
5/96
03/1
3/97
09/2
9/97
04/1
7/98
11/0
3/98
05/2
2/99
12/0
8/99
06/2
5/00
01/1
1/01
07/3
0/01
20-d
ay M
ovin
g A
nn
ualize
d V
ola
tility
$-
$1
$2
$3
$4
$5
$6
$7
$8
$9
$10
Pri
ce (
$/M
Mb
tu)
Prompt NYMEX VolatilityPrompt NYMEX Price
Historical Simulation Cont.
Methodology:1. Select historic dataset as a proxy for the future
2. Subject existing portfolio to historic data return distribution, revaluing the portfolio at each step
3. As with MC simulation – find the loss at your confidence level from the resultant P/L distribution
Stress Testing
Benefits:1. Same as historical simulation, generally
2. Allows management to specify a price environment to stress the portfolio
Weaknesses:1. Allows management to specify a price
environment to stress the portfolio
2. “Grounded in reality” is a matter of perception
Principal Components Analysis w/ MC Simulation
Benefits:1. Handles highly correlated datasets very well
2. Reduces the number of simulated underlying risk factors
3. Full portfolio valuation – handles non-linear (options) instruments well
Weaknesses:1. Not as fast as analytic approach
2. Can’t develop VaR “Greeks”
3. “Black Box” effect
Principal Components Analysis w/ MC Simulation Cont.
Good fit for BP Energy’s natural gas position• 63 natural gas delivery locations in North
America• Majority of trading activity in first 13 months or so.
• Analytic or MC Correlation matrix = 819 x 819 = 670,761 elements – very highly correlated – a statistical nightmare!
• Embedded optionality in many positions• Requires a full portfolio valuation approach to
capture the “Greeks”
Principal Components Analysis w/ MC Simulation Cont.
Methodology:1. Extract principal components, or independent normally
distributed return factors, from historic dataset
2. Simulate the the principal components to generate forward curve changes
3. Revalue the portfolio under each iteration of forward curve change
4. As with MC simulation – find the loss at your confidence level from the resultant P/L distribution
Principal Components Analysis w/ MC Simulation Cont.Natural Gas PCA underlying dataset:
Dates NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - CloseNatural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)
4/18/1996 2.331 2.337 2.332 2.302 2.262 2.257 2.287 2.365 2.37 2.27 2.085 1.917 1.912 1.907 1.907 1.907 1.9084/19/1996 2.361 2.366 2.357 2.326 2.28 2.272 2.3 2.38 2.385 2.28 2.095 1.926 1.92 1.915 1.915 1.915 1.9164/22/1996 2.359 2.364 2.364 2.339 2.296 2.29 2.318 2.403 2.41 2.295 2.103 1.928 1.922 1.917 1.917 1.917 1.9184/23/1996 2.28 2.293 2.3 2.294 2.267 2.264 2.292 2.375 2.385 2.27 2.078 1.903 1.897 1.892 1.892 1.892 1.8934/24/1996 2.214 2.258 2.26 2.26 2.235 2.235 2.27 2.355 2.368 2.25 2.06 1.887 1.883 1.882 1.882 1.882 1.8834/25/1996 2.258 2.242 2.238 2.212 2.212 2.252 2.332 2.345 2.225 2.035 1.862 1.858 1.857 1.857 1.857 1.858 1.8884/26/1996 2.207 2.213 2.205 2.183 2.183 2.229 2.305 2.318 2.213 2.025 1.858 1.857 1.857 1.857 1.857 1.857 1.8854/29/1996 2.223 2.204 2.198 2.177 2.177 2.22 2.3 2.313 2.213 2.03 1.873 1.872 1.872 1.872 1.872 1.872 1.8994/30/1996 2.224 2.198 2.191 2.173 2.175 2.225 2.305 2.318 2.223 2.04 1.885 1.884 1.884 1.884 1.884 1.884 1.9115/1/1996 2.229 2.214 2.209 2.192 2.192 2.242 2.322 2.332 2.245 2.07 1.92 1.921 1.923 1.923 1.923 1.923 1.9485/2/1996 2.19 2.191 2.185 2.163 2.168 2.218 2.301 2.312 2.237 2.081 1.951 1.951 1.951 1.951 1.951 1.951 1.9715/3/1996 2.131 2.139 2.14 2.123 2.13 2.183 2.268 2.28 2.22 2.08 1.96 1.96 1.96 1.96 1.96 1.96 1.985/6/1996 2.148 2.164 2.155 2.13 2.135 2.188 2.275 2.287 2.23 2.092 1.98 1.98 1.98 1.98 1.98 1.982 2.0055/7/1996 2.187 2.223 2.205 2.17 2.172 2.218 2.3 2.31 2.245 2.102 1.987 1.987 1.987 1.987 1.987 1.987 2.01
1/31/2003 5.605 5.345 5.027 4.899 4.879 4.859 4.804 4.799 4.917 5.022 5.087 4.944 4.724 4.344 4.191 4.149 4.1542/3/2003 5.766 5.485 5.163 4.993 4.963 4.928 4.87 4.855 4.973 5.078 5.14 5 4.78 4.385 4.22 4.175 4.182/4/2003 5.762 5.512 5.212 5.049 5.009 4.969 4.909 4.894 5.019 5.134 5.201 5.057 4.835 4.416 4.236 4.176 4.1762/5/2003 5.644 5.414 5.171 5.061 5.014 4.969 4.909 4.904 5.046 5.166 5.244 5.104 4.889 4.464 4.289 4.239 4.2442/6/2003 5.828 5.578 5.298 5.158 5.093 5.033 4.968 4.958 5.083 5.203 5.273 5.133 4.905 4.455 4.27 4.22 4.222/7/2003 6.043 5.78 5.448 5.283 5.208 5.138 5.068 5.058 5.183 5.298 5.368 5.228 4.988 4.518 4.328 4.278 4.273
2/10/2003 5.852 5.617 5.327 5.197 5.142 5.082 5.022 5.022 5.162 5.287 5.357 5.225 4.995 4.525 4.345 4.295 4.292/11/2003 5.977 5.722 5.417 5.272 5.217 5.157 5.102 5.102 5.242 5.377 5.442 5.302 5.067 4.557 4.367 4.317 4.3122/12/2003 5.785 5.56 5.315 5.205 5.164 5.116 5.069 5.074 5.224 5.377 5.447 5.312 5.082 4.572 4.382 4.332 4.3222/13/2003 5.74 5.55 5.35 5.26 5.23 5.185 5.145 5.155 5.305 5.455 5.53 5.39 5.155 4.625 4.43 4.37 4.3552/14/2003 5.851 5.644 5.439 5.344 5.324 5.284 5.244 5.259 5.409 5.559 5.639 5.497 5.262 4.702 4.502 4.437 4.422
Principal Components Analysis w/ MC Simulation Cont.Natural Gas PCA results:
Eigen ValuesF1 F2 F3
Eigen Value: 0.0103 0.0012 0.0002 Variance (%) 86.7% 9.8% 2.0%Cumulative (%) 86.7% 96.5% 98.5%
Eigen Vectors
FEB 0.455284 -0.485427 0.360784MAR 0.412056 -0.387287 0.181597APR 0.321384 -0.135265 -0.10103MAY 0.260764 -0.037553 -0.27311JUN 0.227856 0.039848 -0.33875JUL 0.213105 0.066264 -0.31856AUG 0.201009 0.082781 -0.28562SEP 0.190895 0.097382 -0.25817OCT 0.181146 0.117005 -0.22419NOV 0.162593 0.127384 -0.14102DEC 0.149436 0.139668 -0.08145JAN 0.141895 0.143573 -0.04404FEB 0.140349 0.154909 -0.02296MAR 0.139832 0.170801 0.01453APR 0.129057 0.19359 0.112487MAY 0.12583 0.207628 0.140506JUN 0.122726 0.214065 0.154115JUL 0.120056 0.217761 0.163537AUG 0.119295 0.217062 0.170479SEP 0.117425 0.219017 0.186745OCT 0.115155 0.215751 0.199751NOV 0.109022 0.215455 0.201155DEC 0.103991 0.211066 0.197997JAN 0.102727 0.206659 0.204305
January
Eigen ValuesF1 F2 F3
Eigen Value: 0.0107 0.0007 0.0000 Variance (%) 93.2% 6.0% 0.3%Cumulative (%) 93.2% 99.2% 99.5%
Eigen Vectors
FEB 0.301791 -0.386739408 -0.30426MAR 0.289281 -0.370925675 -0.18528APR 0.267494 -0.330572504 -0.10229MAY 0.258825 -0.278897924 0.001271JUN 0.235983 -0.17270135 0.116535JUL 0.216933 -0.091371034 0.193058AUG 0.210146 -0.05878705 0.210769SEP 0.207935 -0.012111404 0.231448OCT 0.206124 0.03469249 0.243369NOV 0.19853 0.102297972 0.243661DEC 0.193315 0.135454562 0.24138JAN 0.189531 0.14454585 0.21112FEB 0.186549 0.154298409 0.183328MAR 0.183167 0.162931468 0.143526APR 0.180479 0.164067994 0.104102MAY 0.176693 0.169296441 0.054528JUN 0.166414 0.181342192 -0.03719JUL 0.158443 0.179255835 -0.07044AUG 0.155079 0.18404749 -0.12844SEP 0.156373 0.195013846 -0.17739OCT 0.159401 0.206647744 -0.23453NOV 0.165147 0.220484995 -0.30494DEC 0.1666 0.224652249 -0.32828JAN 0.165753 0.220127913 -0.33803
June
Principal Components Analysis w/ MC Simulation Cont.
Natural Gas PCA results:
J anuary
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 6 12 18 24
F1 F2 F3
June
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 6 12 18 24
F1 F2 F3
Principal Components Analysis w/ MC Simulation Cont.
Natural Gas PCA results:
Implied Forward Volatility Structure
0%
10%
20%
30%
40%
50%
60%
70%
80%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Months to Maturity
January
June